Models of Quantum Dissipation
The main problem to address to study dissipation at the quantum level is the way to envisage the mechanism of irreversible loss of energy. Quantum mechanics usually deal with the Hamiltonian formalism, where the total energy of the system is a conserved quantity. So in principle it would not be possible to describe dissipation in this framework.
The idea to overcome this issue consists on splitting the total system in two parts: the quantum system where dissipation occurs, and a so-called environment or bath where the energy of the former will flow towards. The way both systems are coupled depends on the details of the microscopic model, and hence, the description of the bath. To include an irreversible flow of energy (i.e., to avoid Poincaré recurrences in which the energy eventually flows back to the system), requires that the bath contain an infinite number of degrees of freedom. Notice that by virtue of the principle of universality, it is expected that the particular description of the bath will not affect the essential features of the dissipative process, as far as the model contains the minimal ingredients to provide the effect.
The simplest way to model the bath was proposed by Feynman and Vernon in a seminal paper from 1963. In this description the bath is a sum of an infinite number of harmonic oscillators, that in quantum mechanics represents a set of free bosonic particles.
Read more about this topic: Quantum Dissipation
Famous quotes containing the words models, quantum and/or dissipation:
“Friends broaden our horizons. They serve as new models with whom we can identify. They allow us to be ourselves—and accept us that way. They enhance our self-esteem because they think we’re okay, because we matter to them. And because they matter to us—for various reasons, at various levels of intensity—they enrich the quality of our emotional life.”
—Judith Viorst (20th century)
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“The student may read Homer or Æschylus in the Greek without danger of dissipation or luxuriousness, for it implies that he in some measure emulate their heroes, and consecrate morning hours to their pages.”
—Henry David Thoreau (1817–1862)